Problem: Simplify the following expression: $ p = \dfrac{-1}{4} - \dfrac{q - 1}{-10} $
In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-10}{-10}$ $ \dfrac{-1}{4} \times \dfrac{-10}{-10} = \dfrac{10}{-40} $ Multiply the second expression by $\dfrac{4}{4}$ $ \dfrac{q - 1}{-10} \times \dfrac{4}{4} = \dfrac{4q - 4}{-40} $ Therefore $ p = \dfrac{10}{-40} - \dfrac{4q - 4}{-40} $ Now the expressions have the same denominator we can simply subtract the numerators: $p = \dfrac{10 - (4q - 4) }{-40} $ Distribute the negative sign: $p = \dfrac{10 - 4q + 4}{-40}$ $p = \dfrac{-4q + 14}{-40}$ Simplify the expression by dividing the numerator and denominator by -2: $p = \dfrac{2q - 7}{20}$